Several results on bounds for the energy of a graph have been considered in the theory. e.g. [1]}, [2]}, [3]}. A tool to give general bounds is given by the so-called spectral moments of a graph [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. The \(k\) -th spectral moment of a graph is given by
\(M_k(G)= \sum \limits _{i=1}^n \lambda _i^ k.\) 
